Home

Research

Teaching

The goal of this seminar is to cover various constructions of p-adic L-functions on the analytic side and understand how they differ. This seminar took place during summer and fall 2010.

Here are some lecture notes (v0.349, imperfect version). They will be updated as the seminar goes on. Comments, corrections, and suggestions are very welcome.

	When & where	Speaker	Topic	Refs
1	Jul. 22, 11am MCS 153	Rob H.	Deligne's conjecture on special values of L-functions	[D79]
2	Jul. 26, 11am MCS 153	Rob H.	Coates–Perrin-Riou conjecture on p-adic L-functions of good ordinary motives, Part I	[Co89a][Co91][Co89b][CoPR89][1]
3	Aug. 5, 9am MCS 153	Rob H.	Coates–Perrin-Riou conjecture on p-adic L-functions of good ordinary motives, Part II	[Co89a][Co91][Co89b][CoPR89][1]
4	Aug. 11, 11am MCS 153	Ander	p-adic measures, pseudo-measures, h-admissible measures, p-adic distributions, Part I	[Co89a][Cz99][Cz-FRpL][MzSwD74]
5	Aug. 23, 11am MCS 153	Ander	p-adic measures, pseudo-measures, h-admissible measures, p-adic distributions, Part II	[Co89a][Cz99][Cz-FRpL][MzSwD74]
6	Aug. 27, 11am MCS 153	Chan-Ho	p-adic L-functions of Dirichlet characters	[Wa-ICF]
7	Sep. 1, 11am MCS 153	Glenn	p-adic L-functions of Hecke characters over totally real fields	??
8	Sep. 10, 2pm MCS 180	Rob P.	One- and two-variable p-adic L-functions of modular forms, Part I	??
9	Sep. 13, 10:15am MCS 153	Rob P. / Rob H.	One- and two-variable p-adic L-functions of modular forms, Part II/Relation to Coates–Perrin-Riou Conjecture	??
10	Sep. 20, 10:15am MCS 153	David	Serre's construction of p-adic L-functions for Dirichlet characters	[Se73]
11	Sep. 27, 10:15am MCS 153	Rob H.	The Eisenstein measure construction for Dirichlet characters, Part I	[Ka77]
12	Oct. 4, 10:15am MCS 153	Rob H.	The Eisenstein measure construction for Dirichlet characters, Part II	[Ka77]
13	Oct. 18, 10:15am MCS 153	Jay	Katz p-adic L-functions of Hecke characters of CM fields, Part I	[Ka78] [HiTi93]
14	Oct. 25, 10:15am MCS 153	Jay	Katz p-adic L-functions of Hecke characters of CM fields, Part II	[Ka78] [HiTi93]
15	Nov. 1, 10:15am MCS 153	No meeting	Number theory day off!	--
16	Nov. 8, 10:15am MCS 153	Jay via Rob H.	Katz p-adic L-functions of Hecke characters of CM fields, Part III	[Ka78] [HiTi93]
17	Nov. 15, 10:15am MCS 153	Myoungil	Panchishkin's approach to h-admissible measures	[Pan02] [Pan03]
18	Nov. 22, 10:15am MCS 153	Ander	p-adic L-functions and formal groups (d'après Katz), Part I	[Ka77b] [Ka81]
19	Nov. 29, 10:15am MCS 153	Joël Bellaïche (Brandeis)	Symmetric square p-adic L-function and ramification locus of the eigencurve (after Walter Kim)	[Ki06]
20	Dec. 6, 10:15am MCS 153	Ander	p-adic L-functions and formal groups (d'après Katz), Part II	[Ka77b] [Ka81]

[Co89a]	John Coates, On p-adic L-functions, Séminaire Bourbaki, Vol. 1988/89
[Co89b]	John Coates, p-adic L-functions attached to motives over Q II, Bol. Soc. Brasil. Mat., 1989
[Co91]	John Coates, Motivic p-adic L-functions, in "L-functions and arithmetic", Durham proceedings, 1991
[CoPR89]	John Coates and Bernadette Perrin-Riou, p-adic L-functions attached to motives over Q, in "Algebraic number theory", Conference in honor of Iwasawa, 1989
[Cz99]	Pierre Colmez, Fonctions L p-adiques, Séminaire Bourbaki, Vol. 1998/99
[Cz-FRpL]	Pierre Colmez, Fontaine’s rings and p-adic L-functions
[D79]	Pierre Deligne, Valeurs de fonctions L et périodes d'intégrales, in Corvallis proceedings, 1979
[Hi-SGL]	Haruzo Hida, On the search of genuine p-adic modular L-functions for GL(n), Mémoires de la SMF, 1996
[HiTi93]	Haruzo Hida and Jacques Tilouine, Anti-cyclotomic Katz p-adic L-functions and congruence modules, Ann. Sci. de l'ÉNS, 1993
[Ka77]	Nick Katz, The Eisenstein measure and p-adic interpolation, Amer. J. Math., 1977
[Ka77b]	Nick Katz, Formal groups and p-adic interpolation, in Journées Arithmétiques de Caen, 1977
[Ka78]	Nick Katz, p-adic L-functions for CM fields, Inv. Math., 1978
[Ka81]	Nick Katz, Another look at p-adic L-functions for totally real fields, Math. Ann., 1981
[Ki06]	Walter Kim, Ramification points on the eigencurve and the two variable symmetric square p-adic L-function, Ph.D. thesis, UC Berkeley, 2006
[MzSwD74]	Barry Mazur and Peter Swinnerton-Dyer, Arithmetic of Weil curves, Inv. Math., 1974
[Pan02]	Alexei Panchishkin, A new method of constructing p-adic L-functions associated with modular forms, Mosc. Math. J., 2002
[Pan03]	Alexei Panchishkin, Sur une condition suffisante pour l'existence de mesures p-adiques admissibles, J. Théor. Nombres Bordeaux, 2003
[Ri79]	Ken Ribet, Report on p-adic L-functions over totally real fields, Journées Arithmétiques de Luminy, 1979
[Se73]	Jean-Pierre Serre, Formes modulaires et fonctions zêta p-adiques, in Antwerp III, 1973
[Wa-ICF]	Lawrence Washington, Introduction to cyclotomic fields, Springer-Verlag, GTM 83, 1997